资源描述：
《adaptive algorithms in finite forms》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、AdaptiveAlgorithmsinFiniteFormIvanTyukin∗DanilProkhorov†andCeesvanLeeuwen∗AbstractWeproposeanewmethodforthedesignofadaptationalgorithmsthatguaranteesacertainprescribedlevelofperformanceandapplicabletosystemswithnonconvexparameterization.Themainideabehindthemet
2、hodistwo-fold.First,weaugmentthetuningerrorfunctionanddesigntheadaptationschemeintheformofordinarydifferentialequations.Theresultingaugmentationisallowedtodependonstatederivatives.Second,wefindasuitablerealizationofthedesignedadaptationschemeinanalgebraic-integr
3、alform.Duetotheirexplicitdependenceonthestateoftheoriginalsystem,suchadaptationschemesarereferredtoasadaptivealgorithmsinfiniteform,incontrastto(conventional)algorithmsindifferentialform.Sufficientconditionsfortheexistenceoffiniteformrealizationsareproposed.Itissho
4、wnthatourmethodtodesignalgorithmsinfiniteformisapplicabletoabroadclassofnonlinearsystemsincludingsystemswithnonconvexparameterizationandlow-triangularsystems.Keywords:adaptivesystems,performance,nonlinearparameterization,finiteformalgorithms1IntroductionSignifica
5、ntprogressinadaptivecontroltheoryhasbeenmadeintheareasoflinearandnonlinearsystems[3,13,20,26],plantswithrelativedegreegreaterthanone[10,19,18],andsystemswithnonconvexparameterization[17,15].However,thereisstillroomforfurtherdevelopments,asthereareimportantunre
6、solvedproblemsregardingtheissueofperformance,especiallyinthepresenceofnonconvexparameterization.Asexpressedbyasymptoticstabilityofadaptivesystems[26],robustness,andgoodtransientbehavior[14],suitableperformancecanbeprovenundertherequirementofpersistentexcitatio
7、n.Asitisgenerallyobservedinpractice,insufficientexcitationresultsinabsenceofasymptoticstabilityand,asitsconsequence,inpoorpa-rameterconvergence,sensitivitytosmalldisturbancesandpoortransientperformance.Asuitableperformancecriterionisneededtoassuretheefficiencyandq
8、ualityofthesystem.Assubstitutesforperformancecriteria,arXiv:math/0309254v2[math.OC]5Nov2003mostoftheavailableresultsindirectadaptivecontrolwithoutrestrictivepersistentexcitationreq
